Distribution corresponding to classical thermodynamics

A distribution corresponding to classical thermodynamics is constructed. The concept of degrees of freedom is generalized and a concept of temperature-dependent number of collective degrees of freedom is introduced. A relationship between the theory of numbers and mesoscopic physics is established. A geometric interpretation of spinodal as a curve of maximum entropy and as a catastrophe in a quasi-static Caratheodory process is given. A concept of local ideal gas is introduced. The phase transition of fluids to a dispersed system is determined. The distribution obtained is numerically compared with the distribution for a van der Waals gas in the Hougen-Watson diagram.